An Analysis of the Catastrophe Model and Catastrophe Characteristics of Traffic Flow Based on Cusp Catastrophe Theory

—The state of urban road traffic flow shows discontinuity and jumping phenomenon in the process of running. There was a data gap in the collected traffic flow data. Through the data analysis, it was found that the traffic flow state had the characteristics of multimode, mutation, inaccessibility, divergence and hysteresis, which were similar to the mutation characteristics of the basic model of catastrophe theory when the system state changed. The cusp catastrophe model of traffic flow based on traffic wave theory was established by analyzing the movement process of traffic flow. In this model, the traffic density was taken as the state variable, and traffic flow and wave speed were taken as the control variable. Referring to the basic idea of catastrophe theory, the solution method of the model was given, and the structural stability of the traffic flow state was analyzed. Through the critical equilibrium surface equation, the stability of the extreme value of the system potential function can be analyzed, and the bifurcation set equation when the traffic flow state changed can be obtained, which can be used to determine the critical range of the structural stability of the system. This paper discussed and analyzed the changing trend and constraint relationship among the wave speed, traffic density and traffic flow when the traffic flow state changed suddenly in different running environments. The analysis results were consistent with the actual road traffic flow state. A case was given, and the results showed that the cusp catastrophe model could describe the relationship among the three parameters of traffic flow from three-dimensional space, and could effectively analyze the internal relationship of the parameters when the traffic flow state changed. The validity of the model and analysis method was verified. The goal of this paper is to provide an analysis method for the judgment of urban road traffic state.

Analysis of the General Tool Life Function of Cutting Tools by Application of the Catastrophe-Theory

Production technology planning requires information on tool life T and its relation to cutting speed v. As the Taylor formula often cannot be linearized on an lg-lg scale, a general tool life function has been developed for describing a v-T function with a convex-concave part. Using catastrophe theory, an analogy is established between the general tool life function and the cusp catastrophe, allowing topological mapping of the general v-T function. Results were verified by machinability tests in the turning of C35 and C60 conventional and specially deoxidized C-steels during steelmaking. It was found that in the convex-concave section of this function, 2–3 cutting speeds can be selected for a given tool life, which is advantageous for harmonizing tool changes in multi-operation technology.

The Use of Synergetic Methods and the Catastrophe Theory

The state of the global ecosystem is currently approaching a critical point, which affects the socio-economic condition of the society. At the present time, the subject of study of economics and financial sciences should be the study of a world characterized by non-stationary changes; socio-economic and ecological crises, which in themselves are related to the multidimensionality and non-linearity of socio-economic systems. The article builds various models using the theory of catastrophe in the process of global socio-economic development, The Ways of solving them are set, the raised models are solved by the computer program Maple, solutions are given and three-dimensional graphs are constructed. For the purpose of analysis, we have selected a synergetic methodology based on the theory of self-organization of complex systems. Various methods and tools were discussed for modeling the unsustainable development of socio-economic systems of which conceptual-methodological basis is catastrophe theory. The algorithm is defined and a complex of models is built in the article, which allows us to determine the type of macroeconomic indicators, the nature of the dynamics, and to determine the possibilities for the development of crises. In the 21st century, it has become clear that the state of the global ecosystem is approaching to a critical bound and it is reflected on the socio-economic development of the society, in addition, the Covid 19 pandemic made the situation extremely tense. Gradually, we are already approaching to catastrophe with big steps. Given this situation, these types of studies are of particular importance.

Research on the Traffic Flow Control of Urban Occasional Congestion Based on Catastrophe Theory

Aimed at the problem of occasional congestion control, the cusp catastrophe theory is used to establish the catastrophe model of the urban road system under occasional congestion, finding breakpoints and analyzing stability after urban road system catastrophes by constructing the energetic function; based on the catastrophe characteristics of the urban road system, the feasibility method of congestion control is discussed. The results show that the control method of traffic flow based on catastrophe characteristics of the urban road system can effectively improve the efficiency of the road system in theory. Finally, the applicability of the control method based on catastrophe characteristics is analyzed by examples under different occasional congestion situations.

A Novel Dynamic Splitting Method for Production Based on Material Balance Theory and Catastrophe Theory in Tight Gas Reservoirs

Splitting methods play a significant role in the coproduction of tight reservoirs which are characterized by vertical multilayer superimposition. It directly affects the accuracy of reservoir performance analysis and detailed descriptions. However, conventional splitting methods are limited to a few factors and static factors without considering the effect of layer parameter change. In this study, sensitivity analysis was carried out on five factors that affect the production splitting in coproduction wells. The research shows that in the production process, multiple parameters have a direct impact on the production of layers. Different parameters, which have to be included to split production, have different scale effects on layer production. Comparing the results of the KH method with the numerical simulation results, the limitation of the KH method for yield splitting is illustrated. A novel dynamic splitting method for production (DPSM) was proposed. This method is based on two primary methods, which are the multifactor static method for production splitting of gas (GPSM) and water (WPSM) and use the catastrophe theory and material balance equation (MBE) and obtain the final results by iterative method. The advantage of this method is that more accurate results in the production process are obtained by selecting eight factors, which contain 6 static factors and 2 dynamic factors, for research. It is more in line with the production practice that the ultimate results of production splitting vary with the production process. The accuracy and practicality of the results had been verified by numerical simulation. This method has practical significance for production splitting in tight gas reservoirs.